2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145711Let $W$ be a Coxeter group of type $\widetilde{A}_{n-1}$. We show that the leading coefficient, $μ(x, w)$, of the Kazhdan--Lusztig polynomial $P_{x, w}$ is always equal to 0 or 1 if $x$ is fully commutative (and $w$ is arbitrary).Approximately 10 pages, AMSTeXQuantum Algebra20C08, 20F55Leading coefficients of Kazhdan--Lusztig polynomials and fully commutative elementstext